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natalie:)

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## Homework Statement

Is U={f E F([tex]\left|a,b\right|[/tex]) f(a)=f(b)} a subspace of F([tex]\left| a,b \right|[/tex]) where F([tex]\left| a,b \right|[/tex]) is the vector space of real valued functions defined on the interval [a,b]?

## Homework Equations

I know in order for something to be a subspace there are three conditions:

- existence of the zero vector [tex]\Theta[/tex]

- closed under addition

- closed under scalar multiplication

## The Attempt at a Solution

I tried to determine some boundaries for the function (not 1 to 1, all values will be positive, a and b can be any real number). I'm not really sure how to approach it ... i thought maybe if f(a)=0 then f(b) will also =0. But i don't really know how to prove that or the other two conditions.

I would really appreciate someone explaining the steps of how to solve this. Thanks!

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